On the Theory of Killing Orbits in Space-Time

This paper gives a theoretical discussion of the orbits and isotropies which arise in a space-time which admits a Lie algebra of Killing vector fields. The submanifold structure of the orbits is explored together with their induced Killing vector structure. A general decomposition of a space-time in terms of the nature and dimension of its orbits is given and the concept of stability and instability for orbits introduced. A general relation is shown linking the dimensions of the Killing algebra, the orbits and the isotropies. The well-behaved nature of "stable" orbits and the possible miss-behaviour of the "unstable" ones is pointed out and, in particular, the fact that independent Killing vector fields in space-time may not induce independent such vector fields on unstable orbits. Several examples are presented to exhibit these features. Finally, an appendix is given which revisits and attempts to clarify the well-known theorem of Fubini on the dimension of Killing orbits.Comment: Latex, 19 pages, no figur

The principle of equivalence and projective structure in space-times

This paper discusses the extent to which one can determine the space-time metric from a knowledge of a certain subset of the (unparametrised) geodesics of its Levi-Civita connection, that is, from the experimental evidence of the equivalence principle. It is shown that, if the space-time concerned is known to be vacuum, then the Levi-Civita connection is uniquely determined and its associated metric is uniquely determined up to a choice of units of measurement, by the specification of these geodesics. It is further demonstrated that if two space-times share the same unparametrised geodesics and only one is assumed vacuum then their Levi-Civita connections are again equal (and so the other metric is also a vacuum metric) and the first result above is recovered.Comment: 23 pages, submitted to Classical and Quantum Gravit

Mission analysis of solar powered aircraft

The effect of a real mission scenario on a solar powered airplane configuration which had been developed in previous work were assessed. The mission used was surveillance of crop conditions over a route from Phoenix to Tucson to Tombstone, Arizona. Appendices are attached which address the applicability of existing platforms and payloads to do this mission

Photometric support for future astonomical research

The I.A.P.P.P. is described and how that organization can provide photometric support for future astronomical research projects such as the 1982-1984 eclipse of epsilon Aurigae discussed at this workshop. I.A.P.P.P., International Amateur-Professional Photoelectric Photometry, is an organization founded in Fairborn, Ohio by the authors in 1980. Its purpose is to encourage contact between amateur and professional astronomers interested in photoelectric photometry, for their mutual benefit and for the benefit of astronomical research. Aspects dealt with include instrumentation, electronics, computer hardware and software, observing techniques, data reduction, and observing programs. Starting with the June 1980 issue, I.A.P.P.P. has published the quarterly I.A.P.P.P. Communications. The Communications contain articles dealing with all the above aspects of photoelectric photometry, although it does not publish observational results as such. Photoelectric photometry obtained by amateurs is published in the same journals which publish photometry obtained by professionals

Using Bayesian variable selection methods to choose style factors in global stock return models

This paper applies Bayesian variable selection methods from the statistics literature to give guidance in the decision to include/omit factors in a global (linear factor) stock return model. Once one has accounted for country and sector, it is possible to see which style or styles best explains current asset returns. This study does not find compelling evidence for global styles as useful explanatory factors, once country and sector have been accounted for

Self-similar static solutions admitting a two-space of constant curvature

A recent result by Haggag and Hajj-Boutros is reviewed within the framework of self-similar space-times, extending, in some sense, their results and presenting a family of metrics consisting of all the static spherically symmetric perfect fluid solutions admitting a homothety.Comment: 6 page

A novel model for one-dimensional morphoelasticity. Part I - Theoretical foundations

While classical continuum theories of elasticity and viscoelasticity have long been used to describe the mechanical behaviour of solid biological tissues, they are of limited use for the description of biological tissues that undergo continuous remodelling. The structural changes to a soft tissue associated with growth and remodelling require a mathematical theory of ‘morphoelasticity’ that is more akin to plasticity than elasticity. However, previously-derived mathematical models for plasticity are difficult to apply and interpret in the context of growth and remodelling: many important concepts from the theory of plasticity do not have simple analogues in biomechanics.\ud \ud In this work, we describe a novel mathematical model that combines the simplicity and interpretability of classical viscoelastic models with the versatility of plasticity theory. While our focus here is on one-dimensional problems, our model builds on earlier work based on the multiplicative decomposition of the deformation gradient and can be adapted to develop a three-dimensional theory. The foundation of this work is the concept of ‘effective strain’, a measure of the difference between the current state and a hypothetical state where the tissue is mechanically relaxed. We develop one-dimensional equations for the evolution of effective strain, and discuss a number of potential applications of this theory. One significant application is the description of a contracting fibroblast-populated collagen lattice, which we further investigate in Part II

A novel model for one-dimensional morphoelasticity. Part II - Application to the contraction of fibroblast-populated collagen lattices

Fibroblast-populated collagen lattices are commonly used in experiments to study the interplay between fibroblasts and their pliable environment. Depending on the method by which\ud they are set, these lattices can contract significantly, in some cases contracting to as little as 10% of their initial lateral (or vertical) extent. When the reorganisation of such lattices by fibroblasts is interrupted, it has been observed that the gels re-expand slightly but do not return to their original size. In order to describe these phenomena, we apply our theory of one-dimensional morphoelasticity derived in Part I to obtain a system of coupled ordinary differential equations, which we use to describe the behaviour of a fibroblast-populated collagen lattice that is tethered by a spring of known stiffness. We obtain approximate solutions that describe the behaviour of the system at short times as well as those that are valid for long times. We also obtain an exact description of the behaviour of the system in the case where the lattice reorganisation is interrupted. In addition, we perform a perturbation analysis in the limit of large spring stiffness to obtain inner and outer asymptotic expansions for the solution, and examine the relation between force and traction stress in this limit. Finally, we compare predicted numerical values for the initial stiffness and viscosity of the gel with corresponding values for previously obtained sets of experimental data and also compare the qualitative behaviour with that of our model in each case. We find that our model captures many features of the observed behaviour of fibroblast-populated collagen lattices